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- Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y, z)→(0, 0, 0) yz x2 + 4y2 + 4z2A function h(x, y) is defined by h(x,y)=(x^2 y)/(〖7x〗^6+y^3 ). Verify the limit over h(x, y) exists at the origin along y = x^2? In either case write also the reason.Calculate the value of the limit lim(x,y)→(0,0) 22xy/x^2+y^2 as we approach (0,0) along the path γ(t)=(−t,t).
- Use the limit definition to show that the partial derivatives of F(x,y) = with respect to x and y are/aren’t the same any point(a,b). (i.e show that Fx(a,b) =/≠ Fy(a,b))Find the solution of the limit using polar coordinate system. Lim (x,y)->(0,0)√x^2+y^2/x^2+y^2the limit lim(x,y,z)→(0,0,0)[xy+xz+yz]/[x2+y2+z2]
- Verify Green’s Theorem for F⃗ = < 3x2 − 8y2, 4y − 6xy >, where C is the boundary of the region bounded by x = 0 , y = 0 , and x + y = 1 .At what points (x, y, z) in space are the functions in continuous? ƒ(x, y, z) = x2 + y2 - 2z2Use polar coordinates to find the limit of the function as (x, y) approaches (0, 0). f(x,y)= 4xy/squareroot(x^2+y^2)